1. Starting with the canonical form of the position and momentum operators in 3D, derive the generalized 3D commutation relations,
$[x_i, p_j] = i\hbar\delta_{ij}$,
$[x_i, x_j] = [p_i, p_j] = 0$,
where here $i, j = 1, 2, 3$ is a convenient shorthand to indicate the 3 spatial dimensions so
$x_1 = x$, $x_2 = y$, $x_3 = z$, $p_1 = p_x$, $p_2 = p_y$, $p_3 = p_z$, where each of the momenta is defined as usual, $p_x = -i\hbar\frac{d}{dx}$, $p_y = -i\hbar\frac{d}{dy}$, $p_z = -i\hbar\frac{d}{dz}$.